Yes, all tires slip at least a little, all the time. I thought you were a mechanical engineer?
Not sure where you heard that... On a molecular level, I suppose you may have something. Friction is simple the molecular hills and valleys of two objects hitting each other as they go by. In that sense sure, some molecules won't lock together, they'll slide, so you have dynamic friction on those particular molecules.
However, there's a pretty large difference between traction with a tire that's in the static friction zone and a tire that's in the dynamic friction zone. When you "lose" traction, you're entering the dynamic friction zone.
It is possible for a tire to switch between dynamic and static friction so quickly that it's nearly in both states simultaneously. This is because of how tires deform under load and so forth. In that circumstance, you could say that the tire was in both.
But if you're nowhere near losing traction, you're in the static friction zone for that tire.
But I fail to see how keeping one axle from moving at all replicates traction. Maybe it's because I got a degree in electrical engineering instead.
So think of it like this.
The purpose of a differential is to "differentiate" the speeds of your two axles, allowing you to turn without breaking one of your tires lose. If you've never driven a vehicle that has no differential, I invite you to try it.
Unfortunately, because the differential provides a means where the axles can spin at different rates, it also means any loss in resistance on either axle will immediately cause the other axle to receive less torque proportional to that loss in resistance. This is known as the "open diff" condition, because it the axle with the loss in resistance now receives more torque, similar to how a lower resistance wire will flow more current than a higher resistance wire.
The purpose of Torsen, limited slip, and any other differential like these is to allow the wheels to rotate at different speeds during Norman cornering, but to maximize traction by not transferring all power to the wheel with less resistance.
In a Torsen diff, this is accomplished by interlocking gears that can "sense" the torque resistance in the axles. Whichever axle has more resistance receives more power. The bias ratio is the measurement of the maximum ratio of torque in one wheel to the other. If you had an infinite bias ratio, the differential would never default to open diff condition. The way this measurement system works is by exerting a torque on one exile while holding the diff on a resistance type mount, creating a situation where, if the other axle is held, the torque you apply on one axle should equal the torque on the fixed axle divided by the bias ratio. The torque measured on the diff should be the sum of the axle torques.
It's similar to the test setup, except it tests the differential statically, without the need for rotation or centrifugal forces.